Example 5 - Circle of Apollonius

Example 5 - Circle of Apollonius

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The Circle of Apollonius is the locus of points the ratio of whose distance from a pair of fixed points is constant:

 

How do we know this is a circle?

What is the center and radius?

You can always get Geometry Expressions to tell you: draw a circle and set its equation to be the same as the locus equation (copy and paste works fine).  You can then read off the center and radius.